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Impurity Redistribution and Junction 

Formation in Silicon by Thermal 

Oxidation 

By M. M. ATALLA and E. TANNENBAUM 

(Manuscript received January 28, 1960) 

In Ihe process of growing an oxide on doped silicon, electrically active 
impurities near the silicon/silicon dioxide interface are redistributed ac- 
cording to the diffusion coefficients and the distribution coefficient of the 
impurity between the oxide and the semiconductor. An analysis of the phe- 
nomenon predicts that single-junction or two-junction material can be ob- 
tained by oxidation of the surface of a compensated silicon crystal. For para- 
bolic growth of the oxide, the surface concentration is independent of time, 
and the junction depth, gradient and sheet resistivity vary with f*. This has 
been demonstrated experimentally by oxidation of a compensated p-type 
silicon crystal doped with gallium and antimony. 

I. INTRODUCTION 

During the growth of an oxide on a semiconductor surface, the doping 
impurities of the crystal may undergo a redistribution in the semicon- 
ductor in a region near the surface. The extent of the redistribution, 
which may range from a pile-up region to a depletion region, depends on 
the segregation coefficient of the impurity at the semiconductor-oxide 
interface, on its diffusion coefficients in both the semiconductor and the 
oxide and on the rate and time of oxidation. 

To illustrate, consider the case where an impurity is completely re- 
jected by the oxide; i.e., its segregation coefficient k is zero. The result- 
ing concentration gradient will cause diffusion of the impurities back into 
the body of the semiconductor. This is a nonequilibrium problem, where 
the resulting impurity concentration profile will change continuously 
with time. Fig. 1 shows schematically two redistribution profiles for two 
extreme cases of pile-up (A: < 1) and depletion {k > 1). 

It is evident that, with more than one impurity in the semiconductor, 

933 



934 



TUK BELL SYSTKM TECHNICAL JOURNAL, JULY 1900 



^ 



* 1" " 


INITIAL 


\^' 


DOPING 


LEVEL 


1 , 




. _ _- M^ 



PILE-UP- 

k<i 



DEPLETION 

k>i 



>x 



INITIAL 

'SEMICONDUCTOR 

SURFACE 



REDISTRIBUTED 
IMPURITY 



REACTED 

SEMICONDUCTOR 



-GROWN FILM 



SEMICONDUCTOR-FILM 
INTERFACE 

Fig. 1 — Schematic diagram of the redistribution of an impurity, originally 
uniformly dietributed, produced by thermal oxidation of semiconductor surface. 

this process may produce various distribution profiles with single or 
multiple junctions. Fig. 2 illustrates two such possibilities. 

In this paper we will present: (a) an analysis of the impurity redis- 
tribution phenomenon and its application to junction formation, and 
(h) experimental data for the system silicon-sUicon dioxide with gallium 
and antimony as impurities. 



II. THEORY 



In Section 2.1 the pertinent equations and boundary conditions of a 
model of the redistribution process is presented. In Section 2.2, an ap- 



SINGLE --H 
JUNCTION 

(a) 




Fig. 2 — Schematic diagram of the concentration profiles of two impurities 
produced by thermal oxidation : (a) single junction formation; (b) double junction 
formation. 



THERMAL OXIDATION EFFECTS IN SILICON 



93i 



SEMICONDUCTOR 



y = i-bx 



bx 



,=„ 



1 = 

t = 

t 

INITIAL SEMICONDUCTOR 
SURFACE 



Fig. 3 — Coordiimtes and notiitinns used in the analysis of the impurity re- 
dietribution phenomenon. 

proximate solution is given for an important practical case where the 
segregation coefficient of the impurity at the semiconductor-film mter- 
face is negligibly small. In Section 2.3 an approximate solution is given 
for the case of parabolic growth of film thickness with time and for any 
segregation coefficient. In Section III, the above solutions are applied to 
determine some junction characteristics. 

2.1 Model of Redistribution Process 

Fig. 3 shows the coordinates and some of the terminology used below. 
At time t = 0, the semiconduclur boundary corresponds to the plane 
,r = when the film growth process is started. At any time / let the film 
thickness be A^. The corresponding thickness of semiconductor material 
used in producuig this film is bX, where b is a constant. For the system 
silicon-silicon dioxide, b is about 0.44 for the amorphous oxide. Using the 
moving coordinate ?/ ^ x — hX, where ?/ = corresponds to the instan- 
taneous location of the semiconductor-film interface, the diffusion equa- 
tion for any point within the semiconductor takes the form 



dn _ n c* 71 . , dX dn 
'dt ^ Jy- 'dt'dy' 



(1) 



where n is the impurity concentration and D is the diffusion coefficient 
of the impurity in the semiconductor. The term dX/dt is the rate of film 
growth that must he obtained from experimental data. The boundary 
conditions that must be satisfied are: 
i. At ( - 0, 



936 THE BELL SYSTEM TECHmCAL JOURNAL, JULY 1960 

n = no for all values of y, (2) 

where Uq is the initial uniform concentration of impurity in the semi- 
conductor, 
ii. At ?/ = 00 , 

n = no for all values of t, (3) 

for a semi-infinite semiconductor. 

iii. At the moving boundary between semiconductor and film, con- 
servation of impurity must be satisfied. The rate of impurity diffusion 
into the semiconductor is 



W)o' 



For a segregation coefficient k, the rate at which impurities are admitted 
into the oxide is 



kn, 



©■ 



where n, is the instantaneous surface concentration of the impurity in 
the semiconductor.* For conservation of impurity, the sum of the above 
terms must be equal to the impurities in the reacted semiconductor 
7iMdX/dt)]: 

Z)(g^ + n.(6-^)^ = 0. (4) 



'0 dt 

3 



Measurements by Ligenza of the kinetics of oxidation of silicon under 
various conditions have shown that the relation between film thickness 
and time can be represented by the following power expression: 

X™ - Ki, (5) 

where K is the oxidation constant that is dependent on the pressure of 
the reacting gas and on tempei"ature. The temperature dependence is 
exponential. 

The activation energy as well as the exponent m are dependent on the 

* This implicitly assumes that the film growth takes place at the semiconductor- 
film interface. Evidence for such a process has been shown for the oxidation of 
silicon under various conditions.'^ Furthermore, if a film grows at the film gas 
interface, i.e., by migration of the semiconductor atoms or ions through the film, 
and if the diffusion coefficient of the impurity in the film is negligibly small, one 
obtains the case of eifectivcly complete rejection of the impurity by the film. If, 
on the other hand, the impurity diffusion in the film cannot be neglected, one 
must include an additional diffusion equation for the impurity in the film and 
solve it simultaneously with (1). Such a case was not considered in this paper. 



THERMAL OXIDATION EFFECTS IN SILICON 937 

oxidation conditions. For oxidation in oxygen or water vapor at pressures 
of one atmosphere or less, the activation energy is 1.7 ev and m is 2. 
For oxidation in water vapor at high pressures, the activation energy is 
1.0 ev and m i.s 1.0. 

Now one desii-es a solution of the diffusion equation, (1), that satisfies 
the three boundary conditions given, (2), (3) and (4), with tlie oxida- 
tion process as described by (5). Such a general solution was not ob- 
tained. Approximate solutions, however, were derived based on dis- 
carding the diffusion equation, (1), and assuming a time-dependent 
exponential impurity distribution in the semiconductor. Such a solution 
satisfies all the boundary conditions, (2), (3) and (4), as well as the 
condition of conservation of all redistributed impurities.* 

2.2 Impurity Rcdisirihution by a Film Growth X'" = Ki with a Segregation 
Coefficient k ^ 0. 

At any time durmg the process, it is assumed that the impurity dis- 
tribution in the semiconductor follows the following exponential form: 

n - no = (us - no)e~'''\ (6) 

where n^ and A are in general time-dependent. This equation already 
satisfies our second boundary condition, (3). To satisfy the third bound- 
ary condition, (4), one substitutes (6) in (4) and obtains 

Furthermore, for the conservation of impurity, 

(n — 7io) dy = nohX. 



f 

Jo 



Substituting in (6) and integrating, one obtains: 

^il _ 1 ^ (^) X. (8) 

From (7) and (8) one solves for n, and A, which are obtained as func- 
tions of time. It is evident that the first boundary condition, (2), is also 
satisfied : 

Vl= p-\- (P'- 1)* (9) 

"0 



* More recently, Doiicette et ;il., have obtained a rigorous solution for the 
special case of parabolic film growth (m = 2). Conceutration profiles basetl on the 
above approximate solution deviate by less than 10 per cent from exact profiles. 



938 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1960 

and 



A = 



hX 



where 



no 



^ 4D dt ^ 4/) ' 



r^^2/.^2/c«.-i)1 ^Qj 



From the above equations and the distribution equation, (5), oneobtains 
the desired distribution of impurities in the semiconductor as a function 
of time. It is of interest to note that both the surface concentration n, 
and the penetration A/X, where X is the film thickness, are determmed 
by the single parameter P, as defined by (10). Except for a parabolic 
growth of the film, where m = 2, the parameter P is generally de- 
pendent on time; i.e., the surface concentration ti^ and the penetration 
A/X are time-dependent. For parabolic growth, however, the surface 
concentration n, is independent of time and the penetration A/X is also 
independent of time; i.e., the penetration of the redistribution A is 
directly proportional to the film thickness X. For the two practical 
cases of parabolic and linear growth one, therefore, obtains 

P = 1 + —J- (parabolic growth) (11) 



and 



4D 



P = I -\- ^ t (linear growth). (12) 



The temperature dependence of the process appears in the ratio K/D 
for parabohc growth. Since both K and D are exponentially dependent 
on temperature, the process of impurity distribution is also exponentially 
dependent on temperature, w^ith an activation energy equal to the dif- 
ference between the activation energies of the impurity diffusion in the 
semiconductor and the film growth process. 

For illustration, the above equations were used to calculate the sur- 
face concentration of redistributed impurities in silicon when it is 
thermally oxidized in oxygen. The oxidation in this case is parabolic 
(m = 2) and the oxidation constant K is best fitted in the temperature 
range of 900 to 1200°C and atmospheric pressure* by the following ex- 
pression : 

* The oxidation constant K, according to Ligenza,' is proportional to p"-^, 
where p is the oxygen pressure. 



THERMAL OXIDATION EFFECTS IN SILICON 



939 



K = 8.3 X 10"' e''-'^""''' cmVsecond, 



(13) 



where q is the electronic charge, k is Boltzman's constant and T is the 
absolute temperature {h-T/q in this expression is in volts). Using (9), 
(11) and (13), rij/no was calculated for diiferent values of D, the im- 
purity diffusion coefficient in silicon, at various temperatures. The re- 
sults are shown in Fig. 4.* On the 1100°C line, pomts corresponding to 
various impurities are indicated, using the diffusion coefhcients at 1100°C 
reported by Fuller and Ditzenberger/ The broken line shown passing 
through the antimony point corresponds to the effect of temperature 
on surface concentration. It corresponds to an activation energy of 4.0 
ev for the diffusion coefficient. In general, for a diffusion activation 
energy greater than the oxidation activation energy of 1.75 ev, lowering 
the temperature will raise the surface concentration of the redistributed 
impurity, Only when the activation energy of diffusion of an impurity 
equals that of the film growth process does the surface concentration 
become independent of temperature. 



No 




io-'« 



S ,0-15 Z S 10-"> '" ' '0"'^ 

DIFFUSION COEFFICIENT, D, IN CmVsEC 



10" 



Fig. 4 — Calcuhvted ratios of impurity surface concentration to body concen- 
tration (N./Nfi) produced by parabolic oxidation of silicon with zero segregation 
coeflicient. The arrows indicate the surface concentrations predicted for the im- 
puriLiea indicated at 1100°C. The dashed line corresponds to the surface concen- 
trations predicted for antimony at various temperatures. 

* For amorphous silica, b = 0.44. 



940 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1900 

2.3 Effect of Segregation Coefficient (k 9^ 0) on Impurity Redistribution 
for Parabolic Film Growth (m = 2) 

Based on thermodynamic considerations, Thurmond^ has calculated 
the segregation coefficient of various impurites at the interface between 
silicon and amorphous sihcon dioxide. His results are summarized in 
Table I. 

This table indicates that, for most impurities commonly used for 
doping of silicon, the segregation coefficient is small and should produce 
pile-up upon oxidation. Furthermore, for these impurities, the assump- 
tion of complete rejection by the oxide appears reasonable. For alu- 
minum as an impurity, however, one should obtain depletion near the 
silicon surface upon oxidation. 

Table I — Segregation Coefficients of Various Impurities in 
THE System Silicon-Silicon Dioxide 



Segregation Coefficient 


k > 


10» 


k 


= 


lOUo 10-3 


k 


< 


10-3 


k 


< 


10-3 


k 


< 


10-3 


k 


< 


10-3 



k < 10-3 



Impurities 



aluminum (AI2O3) 
boron (BjOj) 
gallium (GaiOj) 
indium (IniOj) 
arsenic (AsaOj) 
phosphorus (P4O10) 
antimony (SbsO<) 



No detailed measurements are as yet available of the segregation 
coefficient of the various impurities in the system silicon-silicon dioxide. 
There is some experimental evidence, however, that supports some of 
Thurmond's predictions. Tracer measurements by E. Tannenbaum on 
silicon doped with radioactive phosphorus have shown that, upon 
oxidation, more than 95 per cent of the phosphorus in the reacted silicon 
remains in the silicon. Measurements on junction formation by the 
oxidation of compensated silicon crystals, as discussed in Section III, 
give evidence for the pile-up of antimony. Similar measurements by 
Doucette indicate the depletion of aluminum. 

For cases where k ^ 0, a solution of the impurity distribution is 
readily obtained for the case of parabolic film growth following the same 
analysis of Section 2.2. The results are as follows: 

n. P' li + fl - 1 + 2fc(P' - 

no 1 + 2k(P' - 1) \ "^ L P" 

and 



»] 



THERRL\L OXIDATION EFFECTS IN SILICON 941 

(14) 



. 1-fc-^ 

bX~ ». _ ^ 

Ho 



where 

p' = 1 + (1 - fc) 



6-K 
4/)' 



It is evident that, by setting k = 0, these expressions reduce to those of 
(9), which is the case of extreme pile-up. For the case of extreme deple- 
tion, one sets k = tw and obtains: 



■^ ^ (15) 

?io 



and 



where P is as defined by (11). 

III. JUNCTION FORMATION BY THERMAL OXIDATION 

3.1 System with Two Impurities; Junction Formation 

We have shown that by growing a fihn on a semiconductor surface one 
may obtain, under certain conditions, pile-up or depletion of an impurity 
near the surface. By proper choice of two impurities, one being a donor- 
type impurity and the other an acceptor-type impurity, it is evident 
that various junction configurations may be obtained. 

In this section we vnW discuss the conditions under which such junc- 
tions may be obtained, and will determine some of their characteristics. 
Use will be made of the results obtained in the previous sections. Hence, 
it is implicitly assumed that there are no interactions between the 
impurities. 

In general, the choice of the unpurities is based on differences in their 
segregation coefficient or on differences in diffusion coefficients or on both. 
In the sihcon-silieon dioxide system, for instance, two interesting pairs 
of impurities are gallium-antimony and phosphorus-aluminum. In the 
gallium-antimony system, both impurities will pile up with nearly zero 
segregation coefficient. Due to the smaller diffusion coefficient of anti- 
mony, however, it will produce larger pile-up. If this difference exceeds 



942 THE BELL SYSTEM TECHNICAL JOURNAL, jrLY 1960 

the initial excess of gallium over antimony in the silicon crystal, a junc- 
tion is obtained (see Fig. 4). In the phosphorus-aluminum system, on 
the other hand, phosphorus vnR pile up while aluminum will be de- 
pleted. Here, again, with proper initial compensation of the silicon 
crystal, a junction may be obtained. 

Consider the case of a crystal uniformly doped with a donor-type 
impurity Ud and an acceptor -type impurity Ua , both with zero segregation 
coefficient at the semiconductor-film surface. If the crystal is mitially 
p-type (i.e., «„ > no) the condition for the formation of a single junction 
upon film growth is that (nd)e > (na)s and, from (9), this sets the fol- 
lowing condition on the initial crystal compensation: 

The resulting distribution profiles will be as shown in Fig. 2(a). In a 
similar fashion, one may set the condition of crystal compensation to 
obtain two junctions as shown in Fig. 2(b). 

To demonstrate some typical characteristics of the obtained junction, 
we will consider only the simple case where the pile-up of one impurity 
can be ignored with respect to the pile-up of the other impurity. If ni 
is the impurity that piles up and nn is the other, the compensation of the 
crystal must be such that Ui > ni , and to obtain a junction one must 
satisfy the following requirement: 

^<Pi+(Fi^- 1)^ (17) 

Now an expre.ssion will be given for the resulting junction depth ijj , 
gradient a, and sheet resistance ps by usmg (6), which describes the 
distribution profile of the impurity tii : 

yj_ bn. In h' -'''), (18) 

\n2 ~ nif 



X UiB — Til 

1 
b 



aX = -i(«. - «i)(^- l), (19) 



and 



1 h 



PsX nu 

Hi 



- [in,. - n,J - {», ^ n,) In (=j4r~)] ■ (20) 



where riu is the surface concentration of the impurity Jii , and is ob- 
tained from (9) ; n is the mobility of the carrier of interest; and q is the 



THERMAL OXIDATION EFFECTS IN SILICON 943 

electron charge. Tlie right-hand sides of the above equations are inde- 
pendent of time but dependent on temperature alone. For the parabolic 
film growth, therefore, the junction depth is directly proportional to film 
thicknes.s, and both junction gradient and sheet resistance arc inversely 
proportional to film thickness. The constants of proportionality, which 
are the right-hand sides of the above equations, are determined by a 
single parameter K/D, which is the ratio of the oxidation constant to 
the diffusion coefficient of the impurity in the semiconductor. 

A point of interest that may be mentioned here is that, for a film 
growth process with well-defined kinetics, it is possible from measure- 
ments of resulting junction characteristics (such as junction depth and 
sheet resistivity) to obtain directly the impurity diffusion constant and 
its activation energy, and also the carrier mobility in the semiconductor. 
This is demonstrated in the followmg section on experimental measure- 
ments in the system silicon-silicon dioxide with gallium and antimony 
as the two impurities. 

3.2 Experimental Results 

All measurements reported here were obtained on silicon with gallium 
and antimony as the doping impurities. The choice of these two impuri- 
ties was made for the following reasons. According to Thurmond's cal- 
culations (Table I) l)oth impurities should be rejected by the oxide, and 
hence both should pile up when the sihcon surface is oxidized. Further- 
more, the diffusion coefficient of antimony is smaller by about two orders 
of magnitude than that of gallium, and hence should produce stronger 
pile-up at the .surface. Also, the diffusion coefficient of gallium is suffi- 
ciently high compared to the oxidation constant that its redistribution 
can be neglected (see Fig. 4). 

We have therefore chosen a silicon crystal that was doped with anti- 
mony to a concentration of 4 X lO'* atoms/cm' and compensated with 
gallium to a higher concentration, making the crystal p-type. The crystal 
was not uniform in resistivity, and small slices with different resistivities, 
but uniform within a slice, could be obtained from different regions of 
the crystal. Two sets of slices were used. The first consisted of only one 
slice with a resistivity of 21 ohm-cm. This was used for the experiment 
at 1050°C, with the sample bemg oxidized m oxygen at one atmosphere 
pres.sure for the periods of 2, 18 and 90 hours. After each run, the junc- 
tion depth and sheet resistivity were measured. The surface was then 
etched off to remove the junction, the sample resistivity was measured 
and the second oxidation run was carried out. This was repeated until 
three sets of measurements were made. The second set of sUces con- 



9-44 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1960 



sisted of two slices of 4 ohm-cm resistivity. These were treated at 1210°C 
also in oxygen at one atmosphere pressure, one for 1 hour and the other 
for 10 hours. For each shce, the junction depth and sheet resistance were 
measured. Furthermore, small mesas were etched out of each slice and 
the junction breakdown voltage was measured. Using Miller's relations' 
between breakdown voltage and junction gradient, the junction gradient 
was obtained. Table II gives a summary of the results. 

Fig. 5 is a plot of the above data, with the oxide film thickness, junc- 
tion depth and sheet resistivity for each temperature being plotted 
versus time of oxidation. The straight lines shown indicate, as pre- 
dicted, a satisfactory fit of the data to a square root time dependence. 
In Table II it is also seen that the junction gradient has approximately 
the same time dependence. According to (18), (19) and (20), the 
parameters yj/X, aX and p^X should be functions of the single ratio 
K/D, which is only dependent on temperature, 

In Table III, the experimental values are given for the parameters 
Vj/X, aX, p,X and X^/t = K at the two temperatures of 1210 and 
1050°C. Using (18), (19) and (20), it is now possible to substitute the 
experimental values of the above parameters to obtain the ratio K/D 
and the diffusion coefficient D for the two temperatures and compare 
with published data. In principle, the same value of the ratio K/D 
should be obtained at any one temperature from all three measurements 
of ijj/X, aX and paX. Such calculations were carried out and the results 
are also shown in Table III. At 1210°C, K/D was found to be 0.18 
and 0.14, from the junction depth and the junction gradient meas- 
urements respectively. To obtain K/D from (20) and the measured 
sheet resistance parameter, peX, one finds a strong dependence of K/D 
on the value assigned to the mobility /i„ . We have instead substituted 
the values of K/D of 0.18 and 0.14, obtamed from junction depth and 
junction gradient measurements, in (20) and obtahied values of ^i„ 
corresponding to the measured parameter p^X. The values of Hn ob- 



Table II — Junction Characteristics of Oxidized p-type 
Compensated Silicon with Gallium-Antimony as Impurities* 



T, "C 


t, hours 


p, ohm-cm 


X, A" 


Yi.A- 


Pe , olim/sq 


Vb 1 volts 


a, cm~' 


1050 


2 


21 


1250 


2800 


2480 








1050 


18 


21 


3800 


10300 


880 


— 


— 


1050 


90 


21 


10500 


26400 


414 


__ 


— 


1210 


1 


3.65 


2100 


15200 


2000 


55 


5.5 X 10=" 


1210 


16 


3.65 


8400 


73700 


520 


85 


1.55 X 102" 



Antimony concentration '^4 X 10'* atoms/cc. 



THERNUL OXIDATION EFFECTS IN SILICON 



945 



o so 







/ 






y 


/ 






/ 


/ 






y 


/ 










/ 


/ 







1 

FILM THICKNESS, X, 
IN ANGSTROMS 









/ 


/" 










/ 




/ 






/ 


J 




/ 




-/ 




y 






■/ 






$/ 






/ 




-J. 









\^ 










\ 


N 








> 


K 










\ 


^V 






N 










A 



10=" 10' 



JUNCTION DEPTH, LJj , 
IN ANGSTROMS 



SHEET RESISTANCE, /^s, 
OH MS/CM 2 



Fig. 5 — Experimental data showing the variations with time of the oxide film 
thickness, the junction depth and the sheet resistance, for gallium-aDtimony 
doped silicon. The stniight lines correspond to t^ dependence. 

tained were 120 and 115 cm'/volt-scconds respectively. Similarly, the 
data weic analyzed and the results are given in Table III. It is to be 
noted that the obtained values of electron mobility ^„ of 97-120 cmV 
volt-second at 4 X lO^Vcm^ concentration are in satisfactory agreement 
with published data (see, for instance, Conwell's review article^). From 
the calculated vahies of K/D and the measured K = X^/i, the diffusion 
coefficients of antimony m silicon at 1050 and 1210°C were obtained and 
are given in Table III. Corresponding values from the Hterature^ are 
also given for comparison. 

The self-consistency of the above results and their fair agreement 
with published data are quite satisfactory considering the many simpli- 
fying assumptions on which the analysis was based. 



Table III — Constants Calculated fhom Measured Parameters 



Measuctd 


Calculated 


T, °C 


Yi/X 


aX, cm-' 


piX, 
oil m- cm 


K, era-/ sec 


K/D 


cmV 
volt-sec 


D, cm'/scc 


1210 
1050 


8.0 
2.6 


1.2 X lO'o 


0.042 

0.037 


1.2 X 10-1' 

2.6 X 10-'^ 


0.18 

0.14 

5.8 


116 
120 

97 


(a) 7 X 10-"* 

(b) 4.5 X 10*'^* 



* PubHshed values (Fuller and Ditzenberger^) : (a) 2.5 X 10""; (b) 5 X 10-'^ 
tip = 40 cmVvolt-sec. 
e,i = 4 X 10'8 atoms/cc. 



946 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 19G0 

IV. CONCLUSIONS 

A model has been presented for the phenomenon of impurity redis- 
tribution in a semiconductor during the thermal growth of a surface 
film. It has been demonstrated experimentally for the silicon-silicon 
dioxide system and satisfactory agreement with the model was ob- 
tained. 

The following are some implications of this phenomenon: (a) Under 
certain conditions it may have significant effect on other processes such 
as conventional diffusion in oxidizing atmospheres, (b) In processes 
involving thermal film growth on junctions, such as thermal oxidation 
of silicon junctions for stabilization purposes, impurity redistribution 
effects can be significant under certain conditions and must be taken into 
consideration, (c) The redistribution phenomenon provides an experi- 
mental tool for determinations of some physical constants such as 
segregation coefficients, diffusion constants and mobilities, (d) One can 
make junctions by this method. However, heavily compensated starting 
materials are needed, which often poses a control problem. 

REFERENCES 

1. Ligeiiza, J, R. and Spitzer, W., to be publiahed. 

2. Atalla, M. M., in Properties of Elemental and Compound Semiconductors, Inter- 

science, New York, 1960, p. 163. 

3. Ligenza, J. R., to be published. 

4. Doucette, E. I., Cooper, N. W. and Mehnert, R. A., to be published. 

5. Fuller, C. S. and Ditzenberger, J. A., J. Appl. Phys., 27, 1956, p. 544. 

6. Thurmond, C. D,, in Properties of Elemental and Compound Semiconductors, 
Interacience, New York, 1960, p. 121. 



7. Miller, S. L., private communication. 

8. Conwell, E., Proc. I.R.E., 46, 1958, p. 1281.